{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DMRG using tensorflow\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "from __future__ import absolute_import, division, print_function\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "import tensornetwork as TN\n",
    "import matrixproductstates as MPS\n",
    "import matrixproductoperators as MPO\n",
    "import DMRG as DMRG\n",
    "import ncon\n",
    "import misc_mps as mmps\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif')\n",
    "import tensorflow as tf\n",
    "tf.enable_v2_behavior()\n",
    "#tf.enable_eager_execution()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initializing an infinite MPS and calculating observables\n",
    "Local observables (e.g. expectation values of one-site operators)\n",
    "can be obtained from calling ```imps.expvals_1site(ops,sites)```.\n",
    "```ops``` is a list of numpy or tensorflow matrices, for example $S^z=\\left(\\begin{matrix}-0.5 & 0\\\\ 0 & 0.5 \\end{matrix}\\right)$ use ```Sz=np.diag([-0.5,0.5])```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<psi|psi>=(1.0000000000000004+0j)\n",
      "check orthogonality conditions (all numbers should be small)\n",
      "[(5.712579120949909e-15+0j), (5.472275030941168e-15+0j), (5.595350734381435e-15+0j), (8.444803585217734e-11+0j)]\n",
      "[(5.675196771839677e-15+0j), (6.197326473542378e-15+0j), (6.5010918070416885e-15+0j), (8.444951922239015e-11+0j)]\n",
      "==========  after changing the state  =============\n",
      "\n",
      "<psi|psi>=(0.9999999999999996+0j)\n",
      "check orthogonality conditions after restoring form (all numbers should be small)\n",
      "[(5.493978135378963e-15+0j), (6.89446800475131e-15+0j), (5.661187635229335e-15+0j), (1.1278932840363945e-12+0j)]\n",
      "[(5.181140002815766e-15+0j), (6.030217899096671e-15+0j), (6.283375852479362e-15+0j), (1.1283696470416297e-12+0j)]\n"
     ]
    }
   ],
   "source": [
    "N,D,d=4,50,2\n",
    "#create in infinite MPS in canonized form\n",
    "#initializing the object for large (D > 50) will take some time; there is an sparse solver\n",
    "#running in the background\n",
    "dtype=tf.complex128\n",
    "imps=MPS.InfiniteMPSCentralGauge.random(d=[2]*N,D=[D]*(N+1),dtype=dtype,minval=-0.5,maxval=0.5)\n",
    "#the norm of the state\n",
    "print('<psi|psi>={0}'.format(imps.norm().numpy()**2))\n",
    "imps.position(len(imps))\n",
    "print('check orthogonality conditions (all numbers should be small)')\n",
    "print([imps.ortho_deviation(imps.get_tensor(n),'l').numpy() for n in range(len(imps))])\n",
    "imps.position(0)\n",
    "imps.position(len(imps))\n",
    "print([imps.ortho_deviation(imps.get_tensor(n),'l').numpy() for n in range(len(imps))])\n",
    "#change the state\n",
    "shape=[imps._tensors[0].shape[0],imps._tensors[0].shape[1],imps._tensors[0].shape[2]]\n",
    "\n",
    "imps._tensors[0]=tf.get_variable(initializer=\n",
    "                                 np.random.random_sample(shape).astype(dtype.as_numpy_dtype),name='n')\n",
    "#restore the canonical form\n",
    "imps.restore_form()\n",
    "\n",
    "print('==========  after changing the state  =============')\n",
    "print()\n",
    "print('<psi|psi>={0}'.format(imps.norm().numpy()**2))\n",
    "#imps.position(len(imps))\n",
    "print('check orthogonality conditions after restoring form (all numbers should be small)')\n",
    "print([imps.ortho_deviation(imps.get_tensor(n),'l').numpy() for n in range(len(imps))])\n",
    "imps.position(0)\n",
    "imps.position(len(imps))\n",
    "print([imps.ortho_deviation(imps.get_tensor(n),'l').numpy() for n in range(len(imps))])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "check orthogonality conditions (all numbers should be small)\n",
      "[(5.028951447418385e-12+0j), (5.31777322172323e-15+0j), (4.817117742118863e-15+0j), (5.493788367075543e-15+0j)]\n",
      "[(6.929646455628165+0j), (5.2287784540969925e-15+0j), (5.2870950208501045e-15+0j), (5.652494287059708e-15+0j)]\n",
      "check orthogonality conditions (all numbers should be small)\n",
      "[(5.302854625724801e-15+0j), (5.889981749885554e-15+0j), (5.9064260253919494e-15+0j), (4.813046505589649e-14+0j)]\n",
      "[(5.6759218284589356e-15+0j), (6.242830002868975e-15+0j), (5.9588774293025176e-15+0j), (6.929646455628165+0j)]\n"
     ]
    }
   ],
   "source": [
    "rimps=imps.get_right_orthogonal_imps(power_method=True)\n",
    "print('check orthogonality conditions (all numbers should be small)')\n",
    "print([rimps.ortho_deviation(rimps.get_tensor(n),'r').numpy() for n in range(len(rimps))])\n",
    "rimps.position(len(rimps))\n",
    "rimps.position(0)\n",
    "print([rimps.ortho_deviation(rimps.get_tensor(n),'r').numpy() for n in range(len(rimps))])\n",
    "\n",
    "limps=imps.get_left_orthogonal_imps()\n",
    "print('check orthogonality conditions (all numbers should be small)')\n",
    "print([limps.ortho_deviation(limps.get_tensor(n),'l').numpy() for n in range(len(limps))])\n",
    "limps.position(0)\n",
    "limps.position(len(rimps))\n",
    "\n",
    "print([limps.ortho_deviation(limps.get_tensor(n),'l').numpy() for n in range(len(limps))])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/martin/PY3_TF_1.13/lib/python3.6/site-packages/tensorflow/python/framework/ops.py:739: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.array(self.numpy(), dtype=dtype)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N,D,d=4,20,2\n",
    "#create in infinite MPS in canonized form\n",
    "#initializing the object for large (D > 50) will take some time; there is an sparse solver\n",
    "#running in the background\n",
    "imps=MPS.InfiniteMPSCentralGauge.random(d=[2]*N,D=[D]*(N+1),dtype=dtype,minval=-0.5,maxval=0.5)\n",
    "#calculate expectation values <S^z[n]>\n",
    "#imps.position(N)\n",
    "Nmax=100 #the number of sites for which to calculate the observables\n",
    "Sz=np.diag([-0.5,0.5]).astype(dtype.as_numpy_dtype)\n",
    "mean_sz=imps.expvals_1site([Sz for n in range(Nmax)],range(Nmax))\n",
    "plt.plot(range(Nmax),mean_sz)\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^z\\rangle$',fontsize=20)\n",
    "plt.draw()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some checks:\n",
    "Below are some checks that an infinite MPS in canonical form should obey."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta1=(1.0000000000000764+7.765396024256296e-17j) (should be close to 1)\n",
      "eta2=(1.000000000000076-1.412330476615293e-16j) (should be close to 1)\n",
      "this should be tiny: (4.747810321542748e-16+0j)\n",
      "this should be tiny: (5.318371745963393e-16+0j)\n"
     ]
    }
   ],
   "source": [
    "N,D,d=5,2,2\n",
    "\n",
    "imps=MPS.InfiniteMPSCentralGauge.random(d=[2]*N,D=[D]*(N+1),dtype=tf.complex128,minval=-.5,maxval=1.5)\n",
    "#compute left and right dominant eigen vectors of the unit-cell transfer-operator\n",
    "eta1,x1=imps.TMeigs('l',numeig=1)\n",
    "eta2,x2=imps.TMeigs('r',numeig=1)\n",
    "print('eta1={0} (should be close to 1)'.format(eta1.numpy()))\n",
    "print('eta2={0} (should be close to 1)'.format(eta2.numpy()))\n",
    "\n",
    "#check if x1,x2 are indeed eigenvectors\n",
    "print('this should be tiny:',tf.linalg.norm(imps.unitcell_transfer_op('l',x1)-x1*eta1).numpy())\n",
    "print('this should be tiny:',tf.linalg.norm(imps.unitcell_transfer_op('r',x2)-x2*eta2).numpy())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run infinite DMRG for the XXZ model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SS-IDMRG  it=10/10, energy per unit-cell E/N=-0.4428200329163641+0.0000000000000000"
     ]
    }
   ],
   "source": [
    "N,D,d=2,10,2 #systemsize, bond dimension, local hilbert space dimension\n",
    "#create an Infinite MPS \n",
    "imps=MPS.InfiniteMPSCentralGauge.random(d=[2]*N,D=[D]*(N+1),dtype=dtype,minval=-0.5,maxval=0.5)\n",
    "#get an MPO, e.g. for the XXZ Heisenberg model\n",
    "impo=MPO.InfiniteXXZ(Jz=1.0*np.ones([N]),Jxy=np.ones([N]),Bz=np.zeros([N]),dtype=dtype)\n",
    "#create an infinite DMRG-simulation \n",
    "idmrg=DMRG.InfiniteDMRGEngine(imps,impo)\n",
    "\n",
    "#run the optimization; the energy per site E/N should be ~-0.443 for Jz=1, Jxy=1 above in MPO\n",
    "idmrg.run_one_site(Nsweeps= 10,verbose=1,ncv=100)\n",
    "#idmrg.mps.canonize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The DMRG engine leaves imps in a non-standard form. Bring the imps back into the standard central form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SS-IDMRG  it=10/10, energy per unit-cell E/N=-0.4429350742740397+0.0000000000000000"
     ]
    }
   ],
   "source": [
    "idmrg.run_one_site(Nsweeps= 10,verbose=1,ncv=30)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "idmrg.mps.restore_form(numeig=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/martin/PY3_TF_1.13/lib/python3.6/site-packages/numpy/core/numeric.py:538: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#calculate expectation values\n",
    "L=12\n",
    "imps.position(1)\n",
    "Sz=np.diag([-0.5,0.5]).astype(np.complex128)\n",
    "\n",
    "mean_sz=idmrg.mps.expvals_1site([Sz for n in range(L)],range(L))\n",
    "mean_sz_=[idmrg.mps.expval_1site(Sz,n).numpy() for n in range(L)]\n",
    "plt.plot(range(mean_sz.shape[0]),mean_sz.numpy(),range(len(mean_sz_)),mean_sz_,'x')\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^z\\rangle$',fontsize=20)\n",
    "plt.legend(['expvals','expval'])\n",
    "plt.draw()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "shift the unitcell by one site and check that state is still OK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==========  after changing the state  =============\n",
      "\n",
      "<psi|psi>=(1+0j)\n",
      "check orthogonality conditions after restoring form (all numbers should be small)\n",
      "[(1.642587180860208e-15+0j), (2.2738612179334534e-12+0j)]\n"
     ]
    }
   ],
   "source": [
    "idmrg.mps.cycle(1)\n",
    "imps.position(1)\n",
    "print('==========  after changing the state  =============')\n",
    "print()\n",
    "print('<psi|psi>={0}'.format(imps.norm().numpy()**2))\n",
    "imps.position(len(imps))\n",
    "print('check orthogonality conditions after restoring form (all numbers should be small)')\n",
    "print([imps.ortho_deviation(imps.get_tensor(n),'l').numpy() for n in range(len(imps))])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_sz_shifted=idmrg.mps.expvals_1site([Sz for n in range(L)],range(L))\n",
    "mean_sz_shifted_=[idmrg.mps.expval_1site(Sz,n).numpy() for n in range(L)]\n",
    "Sx=np.array([[0.0,1],[1,0]]).astype(np.complex128)\n",
    "\n",
    "SzSz_=idmrg.mps.correlator_1site(Sx,Sx,1,50)\n",
    "\n",
    "plt.plot(range(mean_sz_shifted.shape[0]),mean_sz_shifted.numpy(),\n",
    "         range(len(mean_sz_shifted_)),mean_sz_shifted_,'x')\n",
    "plt.plot(range(mean_sz.shape[0]),mean_sz.numpy(),range(len(mean_sz_)),mean_sz_,'x')\n",
    "plt.legend(['expvals','expval','expvals','expval'])\n",
    "\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^z\\rangle$',fontsize=20)\n",
    "plt.draw()\n",
    "plt.show()\n",
    "plt.plot(SzSz_.numpy())\n",
    "plt.ylabel(r'$\\langle S^x[0] S^x[site]\\rangle$',fontsize=20)\n",
    "plt.xlabel('site',fontsize=20)\n",
    "\n",
    "plt.draw()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(2.6125018243622655+0j), (2.637606338343902+0j)]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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N6VmKxdB+euikRgBISkxAYWbwjbZaOvtQlpuGhATxHCsv0Avz7b2e7MPTJqcLh9v78PnZ4zzHRATnlWUHnYti1E+8A8rCCm3+Sn1Th2cggLcPG9uRlWoZ8vMvn1aMP24+DJvDNeQ9AbT/gHW7W3HJ1CLPcxdPKUJWqgX/99FxXDGj2O9nHGjtwcfHuvGDa2d6jv3Nwon4zrqd+LCxHUumFPp9zwsNLegbcOFvl5QDABaU52P+5Dw88W4jvrhoUsCdNB+u24/c9CR8+cJyiAju+9x5uO6/3sPjbzfi7qun+53f1e/AQ6/tw4LyPFw/pwwighvnluHRtw/h2jllmFaSFfD9+u37TfjS4sm46rwSlBdm4LpH3sO3nt2BZ1YsCtiuR944iLo9J/HD62biziXlSLEk4L/ePIiJ+Wm4bcEkv/PtThdW/2Erdh614tE75mNcTirueHIzbl/7IZ5buRgT89P9vudwey/u+M1mtJ8ewJNfrsGL21rwb6/swaG2XvzohllICtCu1z85ge8+vxNJlgT8/ZVT8MS7Tfjcw+/goWVzUDuzxO98h8uNX795CI+8cQD5GcnIz0jG1/+4DVfOKMa/XD8rYLtau2144NW9eGn7MeSkJeH13a34w4dH8I3Lq3DnknK/3y9A64J8eOMBvHvglOf9u2hKAVZeWoVLpxZCRIacb3e68MpHx/H0B834SB+UUpiZjFuqJ2D5gomoKsr0+xknumz4045jeGlbC/a3nkZigmBJVQGuOX8crp5VOqQ7G9A+FOxoseL1T1rx+u4TaGzrRUVhBi6bVoQrZhRjUUW+37V02xz48FA73jt4Cu8dOIXOvgHMn5yPxZX5WFRRgJll2Uj0uh8opdB0qhdbD3di6+FO7DhqRXpyIuZMzMXcibmYMyEXkwvS/a5/OIULKI1R/FmRvFauz+OCM3weIrISwEoAmDTJ/z9jJDzzUIZ0eRl7ojg8Q30NRoZSkDn0ly7U5EZtDsrQ1/EeOuwbUHxHeBlmlWXjuS1H4XKrIb+MgNbdZUkQz5wVAKgqykReehLqmzuwfMFEv3Z9cKgdiyoKhrzWZdOL8Nv3m7CpsR1XTB8aID75tBufdtnw7aXTPMeSLQm4elYpXvvkBOzO2UNqUQDw8vZjSEwQXD+nzHPsc7PH4Yd/3o1n64/6BRS3W+G/NzWjelIuZo8ffF9WX1aFFb9vwCu7juOGueOHXvtRK97c14Z7rp6OzBTtv8H5E3Jw/ZwyPPleI+5YPNkzcMLwnxsPoKNvAL+7bqHnP+kPrp2Jt/e34d4XP8L61UuGfAA4bXfinvU7MSk/Hfd9fobn/f3xTbPxnXU78Z8bD+AfPjM0cG3c04r/qNuPm6vH484lWqD70Q2zccxqw/0vf4xxOWm4VO9mBLQuuO+s24F3D5zCg8suwNWzSgEAz6xYjC8+uRm3Pb4Jz65cjMkFgx8O9hzvxpd/uwVOlxvPrFiMuRNzceWMYvx8wz786s1DONLRi19/YT5y0pM8P+OXdfvxyBsHccGEHDx6x3yMz03DDfPG4/89sx13/b4Bd144Gfd9/jzPTXJ/aw+++/xO7DrWhRvnluGH189CZooFT3/QjF9s2I+l//E2vl07DV+7uAJJiQmwOVz4zXtN+NWbB+F0KXzj8ip884opaG7vxc9e24efvLoXT73fjG/VTsWt8yfAkpiALU0deHjjfrx/sB2Fmcn4/ufPw/Vzy/Dy9mN46v0m3PnbLZhRmoUVl1Tiujll6OgdwB83H8azW47g1OkBVBVl4Ec3zEJZThqebziKJ99rwuPvNGJheT5uWzARl00vwtv72vDS9hZ8cEgb2Th/ch5+dMMsnOiy4ZVdx3HvS7vw/T99jCVVBbj2gnEozkrFhj2tnpqfJUGwuLIA188pw46jVjy75Qie/qAZqUkJWFJViEunFqKjz4H3DrRhZ0sXXG6FtKRELKrMR/XkPNQ3d6BuTysAbYmn+eV5mFWWjf2tp7HtcCfa9UwpO9WC6sl56LU78eyWI3hKX5cvJy1JCzATcvD3V00NuUV5NIQMKEqpe8/kxUSkXCnVHI3X0lkB5J/F81BKrYU24RI1NTVRGRdqc/gX5bO8AoovIz32zlAAoCQ7xVMr8dXS2Y8rphcNOVZeqH2iawqwSOR+fYSX76fkWWU56Hc0o+nUaUwpHvrczqNWnDcue8gnJRHB/Mn5aDjsX5g/Zu3H4fY+3Hlh+ZDj2qetBLy9r80voNTtaYUIcKVPJnLNBeOwfmsL3jtwCledN/jp1u1W+J8dn+LiKYUo8uruS01KxE3zxuOZzUe0EXNenwjf3t+G5vY+fMcraAHAVTOKMbU4E4+93ejJKAwPbzyA3PQk3Llk6LXcc/V0vPrxcfyybj9+essFnuMHT/bgdx804/YFE4cErYLMFPzjNTPx3Rd24o+bD+NLXu/Nj1/Zg5bOfryw6kKkJw/+V7tp3gR8cLAdj7x5EIsqC3CRHiAb207j28/twOzx2fj3m873tDcpMQG//mI1bn1sE77xx21Y//ULMaM0G0opfP/lXfjLrhP4x2vOw/KawQ8As8fn4JkVizyZyjMrFqOiMAP1zR346tP1yEyx4NkVF3p+JxISBPdcPQMVhZm476WPcNOj7+O3dy5AXnoyvrVuO97a14Zb50/Av9442/P7UlWUiZe/uQQP/nUffvNeEzY3deCXt8/FW/va8IvX9yMr1YLH7qjGZ72y5rsuqcTnzx+HH/75E/z01b14edsxfGHRJPzmvSYc6ejDZ2aW4PvXnOcJgLPKcvDUVxZic2M7HvjrXtz30i488U4jirNT8GFjBwozk/GP15yHLy6ajLRkrV2rL6vCVy+qwJ93foon3mnEd1/YiZ+8ugfWPgdcSuGqGcW4c0k5Lp4ymL3UzizByR4bXtp2DOvqj+K7L+z0tHlifhr+/sqpuGneeJR7Ze33XD0dn3zajVd2HccrHx3Hmhd3AQDSkxNx+fQifGZmKa6YXuwJzIBWT9vU2I6397XhrX0n8cbek0gQ4IIJufjG5VW4aEohqiflIdnrw+qJLhs2N7Vjc1MHNje24619bSgvSMfl04tRU56Hmsl5qCrK9HyYcbrc2N96Gh+1WLGzxYodR7vw4rZjfh9ehkO4DCUgEVkBYD4ABWCNUqp78Cm5Wyn1syi1rx6DWUglgA1n+PywCJihpAXfV957YUhvJdmp2Brgxm1zuNDWY/fMkjekJ1swLic1YGH+oD7Cy7ebalaZMWO+e0hAcbsVPmrpwo3zyuBrYUUe6va04mSPDcVZg5/SPfWTKUMTwdSkRCyuLAhYR9mwuxXzJ+WhMDNlyPGLqgqRk5aE//vo+JCAsqW5A8es/fjeZ/1/+f9m4SQ8/UEzXtrWgrsuqfQcf/qDZhRlpeBzXjcuQLtJrry0Eves/whv72/D5Xqw+6jFijf2nhySnRgm5qfjjsWT8bsPmvG1iyswtSQLSin86P/2IC05EXcH+E95c/V4/GnHMTzw132onVmCcTlpeGvfSTy75QhWXVqJmnL/zzz/csMsbD9qxbee24G/fOtipCdbsOq/t8KSKHjsjvl+3SGZKRb89m9rcNOvPsBXnqrHn755EX77fhOeqz+Kv7tiypD3wzCrLMeTqdy+dhP+7sqp+PEru1GWm4b//toiv0waAJbNn4CJeWlY9YetuPHX7yMr1YITXTb8242z8cVFk/y6T1IsifjBtTNx8dRC3P38Tnz2l+8CAD47qxT/dtNsv393ACjLTcPaL9dgw+5W/PP/fIx//vMnmFaSiT98bZGnzuZrUWUBXvz6EtTtOYmfv74PTad6/QKJt2RLApbNn4Bbqsfj7f1teG7LUUzMT8OXFpdjUoF/VxsAFGelYvVlVVh1aSW2NHVgU2M7Lp5SiPmT8wJ2G4kIZo/PwezxOfje1dPx8bFudPYNYGGA7ixDalIirpherH/wmoWjHX3ITk0aEnR8leak4oa54z1Ztt3p8svqvVkSEzCzLBszy7Jx+0KtV2akljuKNP/J1WfEfx16dxKgzTkBsDFa63kppdYDqDSK7XrxHSKyIdTzwy1QUT7UJludvQNIEC399FaanYrOPoffMM9PrcYIL///8BWFGWgKsOqw7wgvw5TiTCRbEvxGejWeOo3TdifmTPDtNYTnBrjVZ/jwB4dOIT8jGdOK/WsFl08rQtOpXhz2atun1n588ml3wP51rdurBBt2tw4ZJfXytmPISE7EZ2aW+n3P9NIsVE/KxTNbjngKu02nevH2/jZ8cdGkIZ/qDDfMHY9xOal47O1DnmMP1x3QayeT/c4HgP935VRkJFs8Q3w37jmJd/a34du101AQ4AYpIvjxjefD6Xbjn/7nE3T1ObDmxY8wrSTTL2sypCdb8KsvVKPH5sB31u3APS/sxKG20/jVF6r9PkgYxuWk4bd/uwDd/Q5c859areeOxZPw3c8E/hkAcN64bDy7YjGcLoUf/OljTC3OwgurLgz4u2VYVFmAP33jIhRkJGPA6cZzKy/EHYsnh+yLv2J6MV799iW4fcFEPHz7XDx6R3XAYOJt6cwSbPiHy7Bu5WL85e8vCRpMDCKCpTNL8NdvX4rN99firksqAwYT3++5fHoxHvvSfHz/mplBg4nv9yyqLMC3a6ehpjzfVA1CRHD+hBxcOq0oaDAJZGJ+eshgEkioYBJMoJrYcIj0p3jfaYYMqdCXZKmJuEU+lFIPKqXq9K4r49jSUM8PN7t+A0wd0uVlbLIVoMurbwC56cl+NYwSvY/+pM9WvccCzEExBFt12HeElyEpMQHTS7L8RnrtOKo9njvRP6DMLstBalIC6r0CilIKmw6148LKgiF1AsNl+qd/7yzF6PtdGiCgAMC1F5ThtN2Jd/TvsTlc+Muu47h6dmnQG8XtCyehsa3X07bfb2pGUqLgC4sC18eSLQn42sUV+LCxAzuOWrGrpQsb957EXRdX+A2eMBijxOr2nMR7B07hX1/ZjSnFmUEDEABMKkjHd2qnYcPuVty2dhPaTw/g57fODXlzmV6ahX+5fhbeP9iOVz8+gfs+d17AAQfeZpZl49d3zIe1bwDXzynDj66fHfaGN700C+tWLcbfXTEFz6xYFDAo+iovzMCr37oUb99zBeZPzgt7PqB9wv/pLRfghrnjTReCM1IsWFRZMOx9+zQyIv1XnOL1tf8dCRi5YQWjINiwYSB4l1degE8hnr3lfQrznjkoAQJKZWEGrH2OIbPAjRFeUwNkDsDgEizewzV3HrUiM8WCygAjWpItCZg7MRcNhwdnzDe39+F4lw0XVvmNewCgZU6TC9KHzEfZsLsVlYUZAUfNAMCFVQXIS0/yzFDfuOckeuxO3DxvQsDzAW3IcVaKBc9tOYJeuxPrG1rwudnjhnTN+bp94SRkp1rw2FuH8PDG/chJ86+d+PrqRRUozU7Fit834HB7H/7p2plhP+V97eIKzByXjb0nevB3V07B+RNyQp4PALctmIgVl1TgqxdV4K5LKsKeDwCXTSvC5vuvwsO3zw0Y3AOZUpyFu6+eHjSIBpJsSTijT9tEkQaUx/VFH8sxNFsxjOlFkYyifLLXDSbZkoC0pMSAXV4dvQMoyPD/VDg4uXFoQDnW2Y/EBPEEHG9GjcR7CZZgI7wMs8qyYe1z4LjXz/moxYrzx+f4ZU2GBeX5+MRrwy3f+SeBXDatCJsOtcPmcKHH5sCHje1BsxNAy54+O7sUdXq318vbW1CSnRI0aAFaV9EN88rwyq7jeOr9JvTYnWGDQ2aKBV++sByv7T6Buj2hsxNDWnIivrN0KvodLiydWTJkZFUwlsQE/NcX5uE7tdPwzSumhD0f0LpKvn/NTPzTdTPPaHhnQWbKiA4HJTIjooCi10pehDYUeI2IfE1ErtT3SbkbQFU0Gxlr7E4XLAnil6Znp1kC7ivf2etAXkbwDMV3LkpLZx9Ks1MDdgMEWiQy2Agvw0yvwrzR/t3Hu4fMP/FVU54Pl1th+xFtrsoHh06hJDsl4NwUw+XTi9DvcKG+uQNv72+Dw6UC1k+8XXN+GXoHXHhp2zG8ta8NN8wdHzTIGf5m4STYnW78YsN+nD8+B9WTgl+H4W8vKkdyYoKWnVxUHvZ8AFh0XZ0CAAAZH0lEQVQ2fyJ+fNNs/PtN55s6HwAqizLxrdqpI9ZnTRRLIv6t12sWNQC6ATwBbULhVmiTIe+LTvNik/d+8t6yUpPQY/fPUHyXrjdkp1mQmpTgF1ACzUExTMxPR2KCDKmj+K7h5WtGaTZEBvdG2XO8Bw6XwtyJwbtkqiflIkHfcMuonyyp8p8k5m1xZQGSLdrw4brdrcjPSEb1pND974sr85GfkYx//8seON0KN80bH/J8QBu9dMGEHLgVPHM1winMTMEDt1yAh5Zd4BlAEU5iguCLiyYPGb5MRMFFNGzYoJTaBm34MEQkRyllbs2Dc5y2/a9/33J2qn+GopTyW7reICL65MahRfmWzv6g3T5JiQmYmJfmE1C0EV7BRn9kpFhQUTi4x/zOADPkfWWlJuG8cdqGW/tbT6O9dyBkVxSgdUctqsjHG3tP4tRpOz4zqzRstmHRu72e2XwEM0qzcN44c3uyffOKKfjNe0249oJx4U/W3WgiWBFR5CLdArjc91i8BBNAW3olUIaSnZbkV0Pptjnhciu/SY2GkuxUtHrVNgacbrR224IOHQW0bi/vGkqwEV7eZpXleDbb2nnUiuKslIA1Gm8LyvOx/YgV7x7QCu2h6ieGy6YVofFUL7pt2mKQZlx7vhYUzGQnhqtnleL5VReyaEwUQyLt8lrje0BEcvQtgsf8nvI2pxspAW5kWan+S9h3BpnUaCjxWX7lRJcNbgVMCDFPoKIwE82neqGU8ozwClY/Mcwqy8Yxaz86ewewo8WKORNzw3YV1ZTnod/hwlPvN2NiflrIIGe4XJ/dn2xJwKXTQg+BNVxYVYC1X5oftrhORLHNVEARkYP6qK6fiMiVgc5RSnUppR4CUBDsnLHC7nAFzlBSLX7DhtvDBJTSHC2gGEN6W6zaCrHBaigAUFGYjn6HC63ddjS2aSO8phSHy1C0rqQPG9vRqG/5G46x4dYxaz+WVJoLDlVFmdqyENOKhiw3EoqI4DOzSpltEJ3jzNZQbgVwG4Cl0LITJSI10Arxryul3jROVEptHGt7yPuyB8lQjC4vpZTn07+ZDGXA6UZXvwO56ckh56AYKgq14NF46jRO6SsZh8tQjAUgn6vXlnMPVT/xbtuk/HQc6ejzW24lGBHBulUXDpn0SUTxwVRA0We/bzcei8jrAIyC/BoRUfrjOgCHoAWel6Le2hihraUTaJSXBQ6Xgs3h9sz07ugLvDCkwXtyY256Mo519kNEW2YjmIqiwVWHT3TZkJggQUd4GQoytZrJO3o95ILx4QMKoHV7Henow4WV5gIKMDi/hojiS6SjvBq9Vw8WkWoAV0ELJJUAfhqFtsUsm8PtWWrFW7ZntrxjMKD0Bl663lCaow1JPdFlw4zSbLR09qMkKzXgulSGcdmpSLEkoKmtF0c7+zC5IN3U+j6zyrJxYq8NlYUZptcPWn1ZFeZOzEUxgwQRhRFpQHnB+4E+fHgbgIfOukXnALvTjcIAN/DstMEFIo0bcGfvAFL0WfSBGEuGGHNRjln7QtZPAG0V3YrCDDS396LxVC+mhqmfGGaVZWPj3pOmursM00qywnanEREBkc+U3xjthpxL7E7XkHW8DEbW0uU1F8XYuyPYiCrfveVbOvtD1k8M5QUZ2Huix9QIL8NMfVMuMwV5IqIzZXaU180iEnbGmYjcYua8c53d4Q5YdA60hL3vZlC+ki0JKMhIRmuPDS63wokuW9gMBdDqKC2d/foaXuYCypIpBbhuTtmQDY+IiKLFbIbyIADPcir6ml2Pish3fQJIHYBVY30uijbKy/+tywmwyVZHkFny3ozJja3dNjjdCuNzw8/38F5Ty2yXV3ZqEh75m3l+W9sSEUWDqYCilJrisz7X/dD2Qfk6gE59jspNXnNR/LePG0OCzUMJtA1wZ+9A0BFehpLsFJzotnmGDJvJUCr1gGJmhBcR0UiIdKb8BqXUvUqpKQCmAtgB4Dci4hKR1wCsiloLY5C2OKS5Lq9gC0N6K81JRWu3Dcf0SY2maih6QDE7wouIaLhFGlDq9Fnzc5VSjUqpNUqpfABXA1gPYHn0mhhb3G6FAVfgtbxSkxKQlCieLi+Hy40em9NUl9ep0wNoOqUHlBDLrhgKMpKRnWox3d1FRDTcIho2rO+Hcp+IXOVzfET2dB9NAy5tc61Ay4SICLK91vPqNCY1hstQ9JFe2490ojAzxdQSJCKC/7htrqlshohoJES8fL2IZMfj8GG7vltjoAwF0IYOd+sZijGpMT9cDUUvku84YkXVGWQcV5lczZeIaCREunz9zQDuF5F2/XG5iKzTR36VR7F9McfmdAFAwFFegDa5sUevoXSEWcfLUKJPbuyxO5lxENE5K9IaSqW+9Ioxmmub/nUdgAfHclAZzFACd0sN6fLq1f42U5Q3mBnhRUQUiyINKFZAW7JeROYByAWwQin1olJqOYBl0WpgrLHrGUpqkAxlSJeXp4YSet2svPQkz9pdofZBISKKZZEGlDyvCY23AVBKqR1ez4/Z3RvtTvMZSsfp0CsNG0QEJdnaIpFmNrEiIopFkRbl1wJ4Q6+hLAXwuM/z6qxaFcNsDr2GEqQon502uMlWZ98AslMtSEoMH7dLs1NxtMPcOl5ERLEo0sUhu5RSNdCWZFmqlPo6AOhzU8oBhN5b9hw2mKEE6/JKQr/DhQGnO+w6Xt6M1YnNzEEhIopFkXZ5AdBWHfYZOlwFLVupP6tWxTC7Z5RXsC4vYz0vxxkFlPPH52BqcSYyUiIeyU1ENKqievfSC/JjmjHKK1hR3tgTpcfmREfvAMpyzS3EuOrSSqy8ZEwvgUZEY1zIDEVE7o7WD4rma42mcEX5LK/1vDr7wi8MaRARJCSM2Z5CIooD4bq8FkTxZ0XztUZN2KK8Z5Mth7YwZJCtf4mIxppwXV6dIrIuCj9HAMyLwuuMunBFeaPL60SXDQNOd9hlV4iIxoqQAUUptXqkGnKuCFuU1wPKkQ5t5eBwC0MSEY0VZzXKKx55ivIhFocEgKZTvQC0ZeaJiOIBA8oZsjvdSEwQWIJMVsxMtkAEONzODIWI4ovpgOKzd3zcsgXZ/teQkCDISrGguV3LUFhDIaJ4YSqgiMhPAWzVv84RkSuHtVUxTNv+N/TblpWa5Fl+haO8iChemM1Q6pVSUwFt2RUATSJy1/A1K3bZna6wOyoahXmLnq0QEcUDswFlm4i8ZgQRfQvgzuFr1iARWSYitSLyvQDP5erPLxORB0aiPWYyFGMuSl5GMkQ4WZGI4oPZgLIS2grDU0TkoIjUA8gbvmZpRGQZ4Nmr3ioitT6nLAeQr5Rar5+/crjbpNVQQmcoxmx5jvAionhiNqA06ptn3auUmgItwDQMY7sMCwA0Gm0AUO39pFJqrVJqrf7Q2DFyCBFZKSINItLQ1tZ21g2yO91Bt/81ZKfpGQoL8kQUR8wGlDoRudtrpNd8DG7/O5xyfR4XBDpJRCoBdCilGn2f04NOjVKqpqio6KwbZHeY6fLSMhSzKw0TEY0FpirGes3kZ16H8gB0RKMBQbqpGo1uLgD5Jl5mmVJqVTTaE47d6Qq7xLxRQ2FAIaJ4EjagiMgKAIcANCilugFAKfVQtBrg1WUVSD0Gs5RKABsCtG+ZUupB/etaPRANG7vTjfyMcF1eWobCSY1EFE/MdHk9D60g3yki60Tk5mFuk4debK80ivFGsBCRDfrftQAeEJGtIrJ1JNpkpijv6fJKTxqJJhERxQQzXV7zATweKCsRkbkA7tMf1gNYa2Qx0WJkHz7Hlup/10HbJXLEmBo2rBfl8zNTRqJJREQxwUyGcmuQYDIP2uz5KmgjvqYA2Cgic6LbxNhiZpRXgR5ISrIYUIgofpjJULqCHL8PgFUpVWMcEJFcAGtF5K5oZyqxwm6iy6tmch6e/soCLKwwM56AiGhsMJOhqCDHa6HVVwZPVMoKYAUGu8HGHDMZiojg8unFnCVPRHHFTEARESn3OXAVgBwEGHWlr/U1Ju+kSim9hhI6QyEiikdhA4pS6l5o3ViTvQ6v0f8ONkQ352wbFovCbf9LRBTPzC6FuxrAiyKioM0LqQKwMkSdZExmKEZACbfaMBFRPDI7U74RQI0+sqsG2iTH7YHO1fdKGZE5ISPNs588MxQiIj9ntFmHHkT8AoleU6mGtphjhVJqQXSaF1uM/eQZUIiI/EXlzqiU2ghgPbQifZOI/CQarxtrPBkKu7yIiPxEbTtBfQHJJ/Q/Y5KNGQoRUVC8M54BFuWJiIJjQDkDLMoTEQUXsstLRB6Fuf1IwhGMgWI9i/JERMGFq6EUKKWWR+MHicjz4c+KbYMZCru8iIh8hfuo7bel7lmI5muNCs9M+TBreRERxaOQGYq+7IoffR8U766wDqXUjkhe61xidHmxKE9E5M/0sGE9iDwIbZXhQM8raGt7rQkXXM5VLMoTEQVn6s6oz4S/H9qikHlKqQTvPwDyoG2w9SCA+/XlV8YczkMhIgrObIZSGao4ry9Z3wWgCdqujSsAvBGF9sUUFuWJiIIz+1G7/Qxf99CZNuRcYHe6kSBAUuKYXEyZiOismA0oVWf4upVn2pBzgbG5FndiJCLyZzag1InIOhG5MsDujdkiUi4ic0XkZhGpxxgYIhyIzeHikGEioiDM7oeyXUTuhVaUXy4igXZk7IK22vByfaHIMcfucLMgT0QUhOlhw3qQWA1gtYhUQNu50WAdq0HEm93pYkGeiCiIkB+3ReTuQMeVUk1Kqe1ef8IGk2CvdS6xO91IZZcXEVFA4e6O0VzM8ZxeGBIYLMoTEZG/cF1enSKyLgo/RwDMi8LrjCqbw8UaChFREOHW8lo9Ug05F7DLi4goON4dzwCL8kREwZkOKCKSPZwNORfYHcxQiIiCMbs45E8BbNW/zhmriz+Gw6I8EVFwZj9u1yulpgKehSCbROSu4WtWbGJRnogoOLN3x20i8poRRPR5J53D16zYpGUoDChERIGYvTuuBLAWwBQROaiv15U3fM2KTXani7s1EhEFYXbplUal1IsAXgRwr4jMA6CGr1mxRynFDIWIKIQzWW34bq+RXvMxRpeoD2bA5YZSQAozFCKigEwFFH3trp8ppbr1QyPW3SUiy0SkVkS+F+a8B4azHXYnt/8lIgol7N1RRFbo+6B45qEopR5SSr00vE3Tgon+8+oAWEWkNsh5tRjmjMnO/eSJiEIyc3d8HlpBvlPfZOvmYW6TtwUY3KyrEUC17wkiUokQG3qJyEoRaRCRhra2togb4tlPnl1eREQBmQko8wE8rpRKVErd5p2Z6Ls0rtP/3D0Ms+lzfR4XBDinUikVNKAopdYqpWqUUjVFRUURN4RdXkREoZkZ5XWrUurrvgf1kV4NALYDWAdgCoCNInKXUmqn2QaIyMoAhxuNbi4A+SG+t1Y/b9jZHHqGwpnyREQBmQkoXUGO3wdtp8Ya44CI5AJYqweV7iDfN4RSam2Ip+sxmKVUQtti2FuHXj/JBVApItVKqW1mfu6Z8mQoXMuLiCggM3fHYPNNaqHVVwZPVMoKYAW0YHPWlFLroQWKWv1xHQCIyAb98Tb9WD78u8eiikV5IqLQzGQoIiLlSqlmrwNXAciBf8YApVSXiEi0GqiUejDAsaU+j9dCGzgwbIyiPGfKExEFFvbjtlLqXmjdWJO9Dq/R/w5Wv8g524bFGhbliYhCM7v0ymoAL4qIgta1VAVgZYg6SdQylFjBojwRUWimAoo+LLdGH9lVA6BBKbU90Ln6Xilbo9fE2MAMhYgoNLMZCgBADyJ+gUSvqVRDm4hYoZRaEJ3mxQ4joLCGQkQUWFQ+biulNgJYD61I3yQiP4nG68YSu9HlxWHDREQBnVGGEoq+6dYT+p8xh11eRESh8e5okpGhJCfyLSMiCiTk3VFfn2vu2f4Qfc2vu8/2dUaTsblWFKfYEBGNKeE+bm8EcL+IHDjTxR9FJFtE7hGRBmgz50dkza3hYne6WZAnIgohZEBRSm1XSi1XSk2FtqbXGyLyWqgl7EXkFhF5HVow6tRX+r1NKbUjuk0fWXani/UTIqIQTN8hlVJP6AtBrgawUEQOisijenfWXBF5TEQOQJunskoptUAp9eRwNXyk2RxujvAiIgrhjEd56aO57gVwrz7/5H5oC0iuVUqtjnL7YoaWobDLi4gomLMaNqzPP9kYpbbENLvDzS4vIqIQeIc0iUV5IqLQGFBMsjlYlCciCoV3SJOMeShERBQY75AmsShPRBQaA4pJWg2FbxcRUTC8Q5qkjfJihkJEFAwDikk2p4sTG4mIQuAd0iTOQyEiCo13SBOUUizKExGFwYBigtOt4FZgUZ6IKATeIU0Y3K2RGQoRUTAMKCbYuJ88EVFYvEOawP3kiYjC4x3SBGM/eXZ5EREFx4BigpGhsChPRBQc75Am2JihEBGFxYBiAmsoRETh8Q5pgiegsMuLiCgo3iFNYFGeiCg8BhQTWJQnIgqPd0gTWJQnIgqPAcUEFuWJiMLjHdIEruVFRBSeZbQbEI6ILANgBVCtlHowwPPVACoBQCm1fjjaYHdyLS8ionBi+g6pBxMopeoAWEWkNsBpq/RAUikilcPRDruDXV5EROHE+h1yAYBG/etGANXeT4rISgBbRaRSKfWgUqrR9wWiweZ0IdmSABEZjpcnIhoTYj2g5Po8LvB5XKX/6RCRx0XE93yIyEoRaRCRhra2togawe1/iYjCG/Uaip5l+Go0urkA5Id5iUNKKauIbAWwEsCQOotSai2AtQBQU1OjImmj3elmQZ6IKIxRDyj6DT+YegxmKZUANgR43gg4udACUNTZnS5OaiQiCiOm75JexfZa/XEdAIjIBq/nc72eDxWcIsYuLyKi8EY9Qwkn0FBhpdTSAM/XDVcb7E4Xu7yIiMLgx24T7E4356AQEYXBu6QJdocbqcxQiIhCYkAxwe50MUMhIgqDd0kTbCzKExGFxbukCSzKExGFx4BigjaxkW8VEVEovEuaYHe6kZrEDIWIKBQGFBOunFGM88fnjHYziIhiWsxPbIwFP7t1zmg3gYgo5jFDISKiqGBAISKiqGBAISKiqGBAISKiqGBAISKiqGBAISKiqGBAISKiqGBAISKiqBCl1Gi3YcSISBuAwxF+eyGAU1Fszrkknq8diO/r57XHL+P6Jyulisx8Q1wFlLMhIg1KqZrRbsdoiOdrB+L7+nnt8XntQGTXzy4vIiKKCgYUIiKKCgYU89aOdgNGUTxfOxDf189rj19nfP2soRARUVQwQyEioqhgQAlDRJaJSK2IfG+02zJS9Ovd4HMsLt4HEcnVr3WZiDzgdTxerr9W/xN3126I12sXkU4R2Xo218+AEoKILAMApVQdAKuI1I5yk0aEfr0ecfY+LAeQr5RaDwAisjJerl9EqgEs1a+zWkQq4+XaDfr1Vepfx9W1A7hVKTVfKbUGiOz6GVBCWwCgUf+6EUD1KLZlNMXN+6CUWquUMoqRlQDqECfXr5TappRaIyK5ABqVUo2Ik2sHABGpxOC1AnF07bpc/T0wnPH1M6CEluvzuGBUWjH64u590P9jdeg31Xi7/hoAVv3reLr2Sv3f2xBP1w4A+QA6RORx/fEZXz8DSmhWaG9yvIvH92GZUmqV/nVcXb/exZGrd3nExbWLSK1vVy/i5NoNenZuhda9FdG/vWVYWjZ21GMwSlcC2BDi3LEsrt4HEVmmlHpQ/7oWcXL9ejH2kN7lZ9xM4uLaoX0yr4V2rZV6PSlerh0ishJaRr4eQLt++IyvnxlKCPqbW2kUowJ8ghmT9E8nNV5Fubh5H/RrfEAf7bIViKvrfxxAo3Fj1T+xxsW16/WjOmhBNFc/FhfXrnseXoV3pdT6SK6fExuJiCgqmKEQEVFUMKAQEVFUMKAQEVFUMKAQEVFUMKAQEVFUMKAQEVFUMKAQjSB9wcUxv3ItxScGFKKRVQtgle9Bn0X5iM5JDChEI0iffV4V4KllI94YoihjQCGKDUtHuwFEZ4sBhWiU6WumjfXNmygOcLVhoijzWvob0BYaXApgDbSFBx8HUKuUEq9zF+hfG1uvGiv+Gq+3EkCH/nABgMd99u0giglcHJIoigKtzKpvWLRGKWXVd0PsNAKK1znK95h+/Hv66z3odewQgPn63hVEMYNdXkTRVQ3/rVI9+0icSRDQg88D3sFEVwdgecQtJBom7PIiiq71ALaKyFIALwCo0/eViEQtvPao8JIPYP5ZtJFoWLDLiyjK9MxiJYDboGUra722Ew7YvRXk2EpoXWWBhhkTxRx2eRFFkYhUK6WsSqkHlVLzAeRB2/XO9DwTEanWg1Ij4mhPczr3MaAQRddt3rPe9ZrJGugjuUyq1INSHRB4Fr2+5zlRTGFAIYq+NT6PK+FVmA+i0StweGclKwA84H2iXlPhCC+KOSzKE0XXIQANXnNRcgFtGLEeMB4AABF5AcAKr1FftwJYJSL1ABqMF1NKrRcRqz5HpV5/zUbOQ6FYxKI8ERFFBbu8iIgoKhhQiIgoKhhQiIgoKhhQiIgoKhhQiIgoKhhQiIgoKhhQiIgoKhhQiIgoKhhQiIgoKhhQiIgoKv4/5z8xEmTm19gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idmrg.mps.cycle(1)\n",
    "imps.position(1)\n",
    "print([imps.ortho_deviation(imps.get_tensor(n),'r').numpy() for n in range(len(imps))])\n",
    "mean_sz_shifted=idmrg.mps.expvals_1site([Sz for n in range(L)],range(L))\n",
    "mean_sz_shifted_=[idmrg.mps.expval_1site(Sz,n).numpy() for n in range(L)]\n",
    "\n",
    "SzSz_=idmrg.mps.correlator_1site(Sx,Sx,1,50)\n",
    "\n",
    "plt.plot(range(mean_sz_shifted.shape[0]),mean_sz_shifted.numpy(),\n",
    "         range(len(mean_sz_shifted_)),mean_sz_shifted_,'x')\n",
    "plt.plot(range(mean_sz.shape[0]),mean_sz.numpy(),range(len(mean_sz_)),mean_sz_,'x')\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^z\\rangle$',fontsize=20)\n",
    "plt.draw()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(SzSz_.numpy())\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^x[0] S^x[site]\\rangle$',fontsize=20)\n",
    "plt.draw()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finite system DMRG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SS-DMRG it=3/10, site=1/51: optimized E=-22.3976601829282984+0.0000000000000000 at D=4600"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: id=172111, shape=(), dtype=complex128, numpy=(-22.3976601829283+0j)>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import time\n",
    "N,D,d=51,100,2\n",
    "mps=MPS.FiniteMPSCentralGauge.random([d]*N,[D]*(N-1),dtype=dtype)\n",
    "mps.position(0)\n",
    "mps.position(len(mps))\n",
    "mps.position(0)\n",
    "mps.normalize()\n",
    "mpo=MPO.FiniteXXZ(Jz=np.ones([N-1]),Jxy=np.ones([N-1]),Bz=np.zeros([N]),dtype=dtype)\n",
    "dmrg=DMRG.FiniteDMRGEngine(mps,mpo)\n",
    "dmrg.run_one_site(verbose=1,Nsweeps=10,ncv=10,delta=1E-10)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/martin/PY3_TF_1.13/lib/python3.6/site-packages/tensorflow/python/framework/ops.py:739: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.array(self.numpy(), dtype=dtype)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#calculate expectation values of z-magnetization\n",
    "Sz=np.diag([-0.5,0.5]).astype(dtype.as_numpy_dtype)\n",
    "Sx=np.array([[0.0,1],[1,0]]).astype(dtype.as_numpy_dtype)\n",
    "mean_sz=mps.expvals_1site([Sz for n in range(3*len(mps))],range(3*len(mps)))\n",
    "SzSz=dmrg.mps.correlator_1site(Sz,Sz,len(mps)//2,3*len(mps))\n",
    "plt.plot(range(3*len(mps)),mean_sz)\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^z\\rangle$',fontsize=20)\n",
    "plt.draw()\n",
    "plt.show()\n",
    "plt.plot(26 + np.arange(SzSz.shape[0]),SzSz)\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^z_{25}S^z_{n}\\rangle$',fontsize=20)\n",
    "plt.draw()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "#apply an spin-s+ operators at site 25\n",
    "Sp=np.asarray([[0,1],[0,0]]).astype(dtype.as_numpy_dtype)\n",
    "mps[25]=ncon.ncon([mps[25],Sp],[[-1,1,-3],[1,-2]])\n",
    "mps.position(0)\n",
    "mps.position(len(mps))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/martin/PY3_TF_1.13/lib/python3.6/site-packages/tensorflow/python/framework/ops.py:739: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.array(self.numpy(), dtype=dtype)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#calculate expectation values of z-magnetization\n",
    "Sz=np.diag([-0.5,0.5]).astype(dtype.as_numpy_dtype)\n",
    "Sx=np.array([[0.0,1],[1,0]]).astype(dtype.as_numpy_dtype)\n",
    "mean_sz=mps.expvals_1site([Sz for n in range(3*len(mps))],range(3*len(mps)))\n",
    "SzSz=dmrg.mps.correlator_1site(Sz,Sz,len(mps)//2,3*len(mps))\n",
    "plt.plot(range(3*len(mps)),mean_sz)\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^z\\rangle$',fontsize=20)\n",
    "plt.draw()\n",
    "plt.show()\n",
    "plt.plot(26 + np.arange(SzSz.shape[0]),SzSz)\n",
    "plt.xlabel('site',fontsize=20)\n",
    "plt.ylabel(r'$\\langle S^z_{25}S^z_{n}\\rangle$',fontsize=20)\n",
    "plt.draw()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
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